Consider the model we used to explain the representativeness heuristics in class (i.e. the Freddy model) and imagine Freddy's psychology is such that: N = 12. Suppose Freddy observes quarters of performance by fund manager Helga. Helga may be a skilled, mediocre or unskilled manager. A skilled fund manager has a 3/4 chance of beating the market each quarter, a mediocre manager has a 1/2 chance of beating the market each quarter and an unskilled manager has a 1/4 chance of beating the market each quarter. Because Freddy is an avid Bloomberg subscriber, he knows these odds. Importantly, in reality the performance of managers are independent from quarter to quarter.

1. (a)Suppose first that Freddy thinks Helga is mediocre. What does Freddy think is the probability that Helga beats the market in the first quarter? Suppose that she actually beats the market on the first quarter. What does Freddy think is the probability she does it again? Suppose that she beats the market again. What does Freddy think is the probability that she will do so a third time?
2. (b)How do the three probabilities in part (a) relate to each other? What sort of psychological bias does this reflect?

(c) Now suppose that Freddy does not know whether Helga is skilled, mediocre or unskilled. He has just observed three consecutive quarters of under performance by Helga. Can he conclude which type of manager Helga is? Can he rule out any of the three type? How many additional rounds he need to conclude something? Explain your intuition...

1. (d)How many more quarters of under performance does Freddy need to observe in order to be sure of Helga's type?
2. (e)Now, let assume that Freddy observes the performance of a large sample of hedge-fund managers over two quarters. The sense of the next part of the exercise is to derive what Freddy concludes about the proportion of skilled, mediocre, and unskilled managers in the population. In reality, all managers in the market are mediocre.
3. Let's compute the proportions that Freddy (and any other trader) observes. What proportion of managers will beat the market twice? What proportion will have two under-performances? What proportion will have mixed performances? .
4. Suppose Freddy though that the proportion of skilled, mediocre, and unskilled man- agers in the population was q , 1 2q , and q , respectively. What does Freddy expect should be the proportion of managers who show two above-market performances in a row?
5. Given your answers to the previous two parts, what does Freddy infer is the propor- tion q of skilled managers in the population? Provide an intuition for your answer